Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations
Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum phy
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Asao Arai
Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations Representation-theoretical Viewpoint for Quantum Phenomena
Mathematical Physics Studies Series Editors Giuseppe Dito, Dijon, France Edward Frenkel, Berkeley, CA, USA Sergei Gukov, Pasadena, CA, USA Yasuyuki Kawahigashi, Tokyo, Japan Maxim Kontsevich, Bures-sur-Yvette, France Nicolaas P. Landsman, Nijmegen, The Netherlands Bruno Nachtergaele, Davis, CA, USA
The series publishes original research monographs on contemporary mathematical physics. The focus is on important recent developments at the interface of Mathematics, and Mathematical and Theoretical Physics. These will include, but are not restricted to: application of algebraic geometry, D-modules and symplectic geometry, category theory, number theory, low-dimensional topology, mirror symmetry, string theory, quantum field theory, noncommutative geometry, operator algebras, functional analysis, spectral theory, and probability theory.
More information about this series at http://www.springer.com/series/6316
Asao Arai
Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations Representation-theoretical Viewpoint for Quantum Phenomena
Asao Arai Department of Mathematics Hokkaido University Sapporo Hokkaido, Japan
ISSN 0921-3767 ISSN 2352-3905 (electronic) Mathematical Physics Studies ISBN 978-981-15-2179-9 ISBN 978-981-15-2180-5 (eBook) https://doi.org/10.1007/978-981-15-2180-5 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
As is well known, canonical commutation relations (CCR) and canonical anticommutation relations (CAR) ar
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